Adding Forces

Motion

What is a resultant force?

The total force acting on an object when all the individual forces are added together, taking their directions into account.

Why are forces vector quantities?

Because they have both magnitude and direction.

What is meant by the magnitude of a force?

The size of the force.

What is the SI unit of force?

The newton (N).

How are forces acting in the same direction combined?

Add their magnitudes together.

How are forces acting in opposite directions combined?

Subtract the smaller force from the larger force.

What direction does the resultant force act when forces oppose each other?

In the direction of the larger force.

What is the resultant of two equal forces acting in opposite directions?

Zero.

What are balanced forces?

Forces that combine to give a resultant force of zero.

What are unbalanced forces?

Forces that combine to produce a non-zero resultant force.

What happens when two forces act at right angles to each other?

Their resultant acts in a third direction and can be found using vector addition.

What does perpendicular mean?

At an angle of 90° to each other.

How can the magnitude of the resultant of two perpendicular forces be calculated?

Using Pythagoras' theorem.

What is the equation for the resultant of two perpendicular forces?

R = √(F₁² + F₂²).

How can the direction of the resultant of two perpendicular forces be calculated?

Using trigonometry.

Which trigonometric relationship is commonly used to find the direction of a resultant force?

tan θ = opposite ÷ adjacent.

How can an angle be found from tan θ?

θ = tan⁻¹(opposite ÷ adjacent).

Why must the direction of a resultant force be stated?

Because force is a vector and therefore requires both magnitude and direction.

How should the direction of a vector angle be described?

State the angle and what reference direction it is measured from, such as 32° above the horizontal.

How can two non-perpendicular forces be added?

Draw the vectors to scale one after the other and draw the resultant from the start of the first vector to the end of the second.

What is a scale vector diagram?

A diagram in which the length and direction of each arrow represent the magnitude and direction of a vector.

What does the length of an arrow represent in a vector diagram?

The magnitude of the vector.

What does the direction of an arrow represent in a vector diagram?

The direction in which the vector acts.

How is the resultant found using a vector triangle?

Draw the vectors head-to-tail; the resultant runs from the start of the first vector to the end of the final vector.

What is the head-to-tail method of vector addition?

Drawing each vector so that the start of the next vector is placed at the end of the previous vector.

What is the parallelogram rule?

A graphical method for adding two vectors by completing a parallelogram and drawing its diagonal.

How do you use the parallelogram rule?

Draw both vectors from the same point, complete a parallelogram using parallel lines, then draw the diagonal from the starting point.

What does the diagonal of a vector parallelogram represent?

The resultant vector.

Can the parallelogram rule be used for forces that are not perpendicular?

Yes. It can be used to add any two vectors in the same plane.

What are co-planar vectors?

Vectors that act in the same plane.

How can more than two vectors be added?

Add two vectors first, then add their resultant to the next vector, continuing until all vectors have been included.

What is a free-body force diagram?

A diagram showing an isolated object and all the forces acting on it.

How are forces represented on a free-body force diagram?

Using arrows.

What does the direction of an arrow on a free-body diagram show?

The direction in which the force acts.

What does the length of an arrow on a free-body diagram show?

The relative magnitude of the force.

Where should force arrows be drawn on a free-body force diagram?

At the points where the forces act on the object.

What should not normally be included in a free-body force diagram?

Other objects; only the object being analysed and the forces acting on it are shown.

Why are free-body force diagrams useful?

They make it easier to identify all the forces and calculate the resultant force.

What is vector addition?

Combining two or more vectors while taking both their magnitudes and directions into account.

Why can forces not always be added using ordinary arithmetic?

Because forces have directions as well as magnitudes.

If two forces of 11 N and 7 N act in the same direction, what is the resultant force?

18 N in the same direction.

If an 11 N force acts right and a 7 N force acts left, what is the resultant force?

4 N to the right.

If perpendicular forces of 110 N and 70 N act on an object, approximately what is the resultant magnitude?

130 N.